The pitch changes because the coffee mug is heating up.
Ever pour coffee into a mug that’s already hot? It doesn’t change pitch when you stir.
If that pot of hot coffee has been sitting there for a couple hours, and I pour it into my cold mug and stir, why are the supposed bubbles fleeing my coffee only now? And how did they manage to stay in my coffee pot all this time? Wouldn’t vigorous stirring actually ADD air to the coffee, if only for a moment?
I think pitch changes according to the height of fluid in the mug, if you stir faster the fluid gets higher, vibrating part of mug is shorter, thus higher pitch. It’s simmilar to bottle percusionist instrument.
As noted previously, this is incorrect. The pitch of your mug of coffee depends on the geometry of the mug, the amount of coffee in it, and the physical properties of both the mug and the coffee. Cecil’s answer is that the physical properties of the coffee are changing; your answer is that the physical properties the mug are changing with temperature.
It is extremely unlikely that the mug material would change enough to make a difference. As a rough calculation, the frequency of the mug is proportional to the square root of Young’s modulus (a measure of material stiffness) divided by the density. Density changes scale closely to changes in the coefficient of thermal expansion (with a factor of three thrown in). From this pdf, we see that, for most ceramics, Young’s modulus scales by a factor between 0.0001 and 0.0004 per degree Kelvin; from here, the CTE of a typical ceramic is 0.000006 - 0.000007 per degree Kelvin. So you can see that, even over a nominal range of 75 degrees Kelvin, Young’s modulus changes by a factor of only 0.03 at best, and density by about 0.0016. Those changes are nowhere near enough to cause two or three octaves pitch change; you should only get a change in pitch of less than 2%.
Although, I should point out as an interesting counterexample, the properties of the shape memory alloy NiTiNOL were discovered, quite serendipitiously, when William Buehler noted the striking change in tone between warm and cool bars of this material. In the case of NiTiNOL, however, the large change (in Young’s modulus, in fact) was the result of a phase change rather than simple continuous change due to temperature. So interesting, but not applicable to the ceramic mug.
The air comes from air bubbles trapped in the instant coffee crystals, or in the creamer powder.
We’ve done this one before. Awhile back, I actually conducted the experiment. My conclusion is that both Cecil and Jearl had some ball droppage on this one, and that temperature is the key factor. I’ll try to see if I can find that thread.
Drat. I can find references to my thread, and even a link to it, but apparently it is kaputski. All my effort for naught.
Short story: I started off with just water and coffee mugs. I found that putting hot water in the mugs caused a pitch shift upwards, which eventually stabilized. I also found that putting cold water in the hot mugs caused a pitch shift downwards, which also eventually stabilized. All of this done with no coffee, hot chocolate, tea, creamer, sugar, etc.
The original post went into a bit more detail, but to be fair I’d have to re-conduct the whole thing to prove it to anyone else, and I don’t feel much like doing it a second time. For anyone who does wish to repeat the experiment, I will advise you that I found the best results came from diner-style thick wall mugs, and the poorest results came from thin wall corelle cups. (I presume that it was because the thinner wall mugs reach thermal equilibrium much more quickly).
To add to your data set: stirring and tapping. I’ve found that when I stir hot liquids (tried with plain water, coffee, hot chocolate, and hot cider) in ceramic mugs, the pitch drops slowly until it reaches a nice, pleasingly deep tone. When I stop stirring, I tap the bottom inside the mug with a spoon and listen to the pitch rise. Renewed stirring deepens it again, and over time the pitch will not drop as low as the initial deep pitch. Also, you can stop the circular motion of the fluid with a sudden spoon sweep, which levels the surface, and the deep pitch does not vanish immediately (the expected result as suggested by daddyCool’s hypothesis) but gradually.
I put it to you that stirring increases the heat transference between the liquid and the ceramic (http://www.straightdope.com/classics/a4_178.html for similar effect of moving air over hot liquid), warming it of course to a certain depth; since ceramic acts naturally as an insulator, the mug does not reach a uniform temperature throughout. When you’re tapping your spoon on cold ceramic, you hear the mere tink of a spoon on ceramic; when you’re tapping your spoon on a partially warmed mug interior, you’ve created an ersatz bell of this ceramic, acoustically united by its difference in temperature from its neighboring ceramic on the one side and the water on the other. It resonates only briefly compared to metal of course, and the cool ceramic exterior has further dampening effect. When you stir your coffee vigorously for a sustained time you are warming the ceramic more deeply and increasing the thickness of your bell wall, thus deepening the pitch.
So we have some folks saying it’s the mug, others the liquid. How about we do an experiment that will help us narrow down which it is?
If we run the hot and cold water over the OUTSIDE of the mug, then we can separate the efects of the liquid being in the mug and affecting the pitch.
Just did this experiment, with several mugs. No discernible change in pitch between the hot and cold mugs. Tentative conclusion: any pitch change is due to chnages in the density of the liquid IN the mug or cup.
BTW heating the mug is most likely to expand it and make it more flexible, both shoul d lead to a LOWERING of the pitch, not raising it.
Stirring the liquid is going to lead to a thinner mass distribution as the liquid climbs the sides, which should raise the pitch.
